F150 Direct or Tensor Matrix Product

Subroutine subprogram MXDIPR computes the direct (sometimes called tensor, or Kronecker) product $C=A\; xB$ of two matrices A and B. Let $A=(a$_ik),(i=1,2,...,I; k=1,2,...K) ; $B=(b$_jl),(j=1,2,...,J;l=1,2,...,L) ; then $C=\; (c$_ij;kl) with $c$_ij;kl=a_ikb_jl . C has $I\; xJ$ rows and $K\; xL$ columns. If, in particular, A and B are square matrices, C is also square.

Structure:

SUBROUTINE subprogram
User Entry Names: MXDIPR

Usage:

    CALL MXDIPR(A,B,C,IAD,JBD,IJD,IA,KA,JB,LB)

A,B

( REAL) Matrices A and B.

C

( REAL) On exit, C contains the direct product $A\; xB$ .

IAD

( INTEGER) First dimension of A.

JBD

( INTEGER) First dimension of B.

IJD

( INTEGER) First dimension of C.

IA,KA

( INTEGER) Number of rows, columns of A.

JB,LB

( INTEGER) Number of rows, columns of B.

Restrictions:

A, B, C must not overlap.

Error handling:

If IA or KA or JB or LB are equal to zero, the subprogram acts as do-nothing.

Examples:

    DIMENSION A(2,2),B(2,2),C(4,4)
    ...
    CALL MXDIPR(A,B,C,2,2,4,2,2,2,2)

$A=($

$a$11	$a$12
$a$21	$a$22

$b$11	$b$12
$b$21	$b$22

$),$

would set

$C=($

$a$11b11	$a$11b12	$a$12b11	$a$12b12
$a$11b21	$a$11b22	$a$12b21	$a$12b22
$a$21b11	$a$21b12	$a$22b11	$a$22b12
$a$21b21	$a$21b22	$a$22b21	$a$22b22

$)\; =($

$c$11;11	$c$11;12	$c$11;21	$c$11;22
$c$12;11	$c$12;12	$c$12;21	$c$12;22
$c$21;11	$c$21;12	$c$21;21	$c$21;22
$c$22;11	$c$22;12	$c$22;21	$c$22;22

$).$

References:

1. E.P. Wigner, Group Theory, (Academic Press, New York 1959) 17
2. W.I. Smirnow, Lehrgang der höheren Mathematik, Vol. III.1, (Deutscher Verlag der Wissenschaften, Berlin 1954) 221

F406